**(1)**The displacement of the particle during the first second of its motion is nearly

**(2)**The average accelerations during the 3

^{rd}second and 7

^{th}second respectively are nearly

^{–2}

**and 2 ms**

^{–2}

^{–2}

**and –2 ms**

^{–2}

^{–2}

**and 2 ms**

^{–2}

^{–2}

**and –2 ms**

^{–2}

**zero and –2 ms**

^{–2}

^{rd}second is the interval from 2 seconds to 3 seconds and during this time the velocity increases from 7 ms

^{–1}to 8 ms

^{–1}. The acceleration is therefore (8 – 7)/1 = 1 ms

^{–2}.

^{th}second is the interval from 6 seconds to 7 seconds and during this time the velocity

*decreases*from 8 ms

^{–1}to 6 ms

^{–1}.

^{–2}. [Option (b)]

**(3)**Which one among the following acceleration–time graphs most closely represents the motion of the particle?

**(4)**Two boys running at uniform speeds

*v*

_{1}and

*v*

_{2}respectively along a straight line path in

*opposite*directions get 9 m closer each second. While running along the

*same*direction with their speeds reduced by 50%, they get 0.5m closer each second. The speeds

*v*

_{1}and

*v*

_{2}are respectively

^{–1}

**and 3 ms**

^{–1}

^{–1}

**and 4 ms**

^{–1}

^{–1}

**and 4.5 ms**

^{–1}

^{–1}

**and 3.5 ms**

^{–1}

**5.5 ms**

^{–1}

**and 3.5 ms**

^{–1}

*v*

_{1}+

*v*

_{2}= 9

*v*

_{1}/2 –

*v*

_{2}/2 = 0.5, from which

*v*

_{1}–

*v*

_{2}= 1

*v*

_{1}= 5 ms

^{–1}

**and**

*v*

_{2}= 4 ms

^{–1}

**(5)**The rear end of a train running on a straight track with uniform acceleration has velocities 6 ms

^{–1}and 10 ms

^{–1}respectively when passing points A and B in its path. The velocity of the rear end midway between these points is approximately

^{–1}

^{–1}

^{–1}

^{–1}

^{–1}

*v*

^{2}=

*u*

^{2}+ 2

*as*where

*u*and

*v*are the initial ans final velocities respectively,

*a*is the acceleration and

*s*is the displacement.

*s*, we have

^{2}= 6

^{2}+ 2

*as*from which 2

*as*= 64

*v*

_{1}is the velocity midway between A and B we have

*v*

_{1}

^{2}= 6

^{2}+ 2

*a*(

*s*/2) = 6

^{2}+ 32 = 68

*v*

_{1}= 8.2 ms

^{–1}nearly.